What is (1-2i)/(2-i)+3-1/2 i ?

The solution to (1-2i)/(2-i)+3-1/2 i is 19/5-11/10 i

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simplify (1-2i)/(2-i)+3-1/2 i

simplify

\frac{1 - 2 i}{2 - i} + 3 - \frac{1}{2} i

\frac{19}{5} - \frac{11}{10} i

Solution steps

\frac{1 - 2 i}{2 - i} + 3 - \frac{1}{2} i

Simplify

\frac{1 - 2 i}{2 - i} : \frac{4 - 3 i}{5}

= \frac{4 - 3 i}{5} + 3 - \frac{1}{2} i

Join

\frac{4 - 3 i}{5} + 3 - \frac{1}{2} i : \frac{i ( - 3 - \frac{5}{2} ) + 19}{5}

= \frac{i ( - 3 - \frac{5}{2} ) + 19}{5}

Rewrite

i (- 3 - \frac{5}{2}) + 19

in standard complex form:

19 + (- 3 - \frac{5}{2}) i

= \frac{19 + ( - 3 - \frac{5}{2} ) i}{5}

Apply the fraction rule:

\frac{a + bi}{c} = \frac{a}{c} + \frac{b}{c} i

= \frac{19}{5} + \frac{- 3 - \frac{5}{2}}{5} i

\frac{- 3 - \frac{5}{2}}{5} = - \frac{11}{10}

= \frac{19}{5} - \frac{11}{10} i

3 (x - 3) + 5 (x + 7) - (x + 1) - 2 (x + 7) + 4 = 0

2 x + 3 \geq 5

25 - 10 x + x^{2}

4^{3} \cdot 4^{12}

\frac{( - 4 a ^{2} b ) ( - 3 a ^{7} b )}{6 a ^{7} b ^{2}} + 16 a^{2}

What is (1-2i)/(2-i)+3-1/2 i ?
The solution to (1-2i)/(2-i)+3-1/2 i is 19/5-11/10 i